Question

parallelogram abcd is rotated to create image abcd. which rule describes the transformation? (x,y)→(y, -x) (x,y)→(-y,x) (x,y)→(-x, -y) (x,y)→(x, -y)

Explanation:

Step1: Analyze point - to - point transformation

Let's take a point, say point A in parallelogram ABCD. If we assume the coordinates of A are $(x_1,y_1)$. In the image A'B'C'D', the coordinates of the corresponding point A' seem to follow the rule where the x - coordinate of the original point becomes the negative of the y - coordinate of the new point and the y - coordinate of the original point becomes the x - coordinate of the new point.

Step2: Check all points

For any general point $(x,y)$ in the original parallelogram, when we apply the transformation $(x,y)\to(y, -x)$, we can see that all the points of parallelogram ABCD are correctly mapped to the points of parallelogram A'B'C'D'. For example, if we consider a point $(2,4)$ in the original figure, after applying the rule $(x,y)\to(y, -x)$, we get $(4,- 2)$ which is consistent with the rotation pattern shown in the graph.

Answer:

A. $(x,y)\to(y, -x)$